A smoothness priors approach to transfer function estimation from stationary time series is shown. An infinite order impulse response model plus an infinite order additive AR noise model is assumed. This is algebraically equivalent to an infinite order ARMAX plus white noise model. A finite order ARMAX model approximation to this model is actually fitted to data. Frequency domain smoothness priors are assumed on the ARMAX polynomials and smoothness hyperparameters balance the tradeoff between the infidelity of the model to the data and the infidelity of model to the smoothness constraints. The likelihood of the hyperparameters is maximized by a least squares gradient search computational procedure. The method is illustrated by the analysis of the Box-Jenkins series J data. Some of the statistical properties of the method are explored in Monte Carlo simulation studies. Keywords: Bayesian models; Linear regression models; Charts.

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